Question: Rewrite as a simplified fraction. ${2.\overline{52} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 252.5252...\\ 1x &= 2.5252...\end{align*}}$ Subtracting the two equations, we have: ${99x = 250}$ ${x = \dfrac{250}{99}} \text{or} {2 \dfrac{52}{99}}$